In 1982 John Hinckley was on trial, accused of having attempted to kill then US President Ronald Reagan. Hinckley was found not guilty by reason of insanity. The defense psychiatric reports found him to be insane while the prosecution reports declared him legally sane. In particular, the defense sought to establish that brain scan results like John Hinckley's appeared in a higher percentage of schizophrenics than of normal people his age.
Throughout Hinckleys trial, an expert witness, Dr. Weinberger, told court that when individuals suffering from schizophrenia were given computerized axial tomography (CAT) scans, the scans showed brain atrophy in 30% of cases compared with only 2% of scans done upon normal people. Health records show that 1.5% of the people in the United States suffer from schizophrenia. Hinckleys CAT scan showed brain atrophy.
Compute the probability that Hinckley suffered from schizophrenia given his CAT scan showed brain atrophy. Do all computations to 5 decimal places and then round at the end to 3 decimals.